From the decades of the theoretical studies, it is well known that the formation of the bar triggers the gas funnelling into the central sub-kpc region and leads to the formation of a kinematically cold nuclear stellar disc (NSD). We demonstrate that this mechanism can be used to identify the formation epoch of the Galactic bar, using an N-body/hydrodynamics simulation of an isolated Milky Way-like galaxy. As shown in many previous literature, our simulation shows that the bar formation triggers an intense star formation for ~1 Gyr in the central region, and forms a NSD. As a result, the oldest age limit of the NSD is relatively sharp, and the oldest population becomes similar to the age of the bar. Therefore, the age distribution of the NSD tells us the formation epoch of the bar. We discuss that a major challenge in measuring the age distribution of the NSD in the Milky Way is contamination from other non-negligible stellar components in the central region, such as a classical bulge component. We demonstrate that because the NSD is kinematically colder than the other stellar populations in the Galactic central region, the NSD population can be kinematically distinguished from the other stellar populations, if the 3D velocity of tracer stars are accurately measured. Hence, in addition to the line-of-sight velocities from spectroscopic surveys, the accurate measurements of the transverse velocities of stars are necessary, and hence the near-infrared space astrometry mission, JASMINE, would play a crutial role to identify the formation epoch of the Galactic bar. We also discuss that the accuracy of stellar age estimation is also crucial to measure the oldest limit of the NSD stellar population.